Curve Editor — Move 2 Handles the same time
To select and move 2 curve handles at the same time you can use simple way which means selecting everything first, and then deselecting what shouldn't be moved.


Select all the curve points which should be edited, set the curve handles type to Free with V > Free.
With MMB deselect curve points and those curve handles which should stay untouched.
Move only one half of curve handles, not moving another.




This works in a similar manner as with editing Bezier curves in 3D View. You can scale, grab those handles etc. 

The disadvantages:


It may be hard to tell exactly which handle belongs to which curve point so in order to select / deselect them correctly.
In case of many curve points to process this may be inefficient.